Article
Mathematics, Applied
Nicholas Aidoo
Summary: In this article, we reduce the complexity in Catlin's multitype techniques for any given sum of squares domain in Cn by providing a complete normalization of the geometry. With this normalization result, we present a simpler proof of the equality between Catlin multitype and commutator multitype for such domains when both invariants are finite. Finally, we reformulate algebraically Catlin's machinery for computing the commutator multitype at the origin for any given sum of squares domain in Cn.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Peter Balazs, Daniel Freeman, Roxana Popescu, Michael Speckbacher
Summary: We formulate a conjecture about frame multipliers in finite dimensions and prove its equivalence to a previous conjecture. Additionally, we provide solutions to the conjecture for certain classes of frame multipliers.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Qiangchang Ju, Jiawei Wang, Xin Xu
Summary: The shallow water magnetohydrodynamic equations with ill-prepared initial data in the small Alfven number limit are proven to converge to the solution of a one-dimensional system coupled with a linear system using the fast averaging method. This method is also applied to study the small Alfven number limit of the three-dimensional ideal incompressible magnetohydrodynamic equations.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Timur Akhunov, Lyudmila Korobenko
Summary: This paper extends the study of hypoellipticity of a class of degenerate elliptic operators, focusing on the gain of derivatives in the non-degenerate part. The authors propose a method that does not require explicit analytic construction.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Manuel Hauke
Summary: In this study, we examined the asymptotic behavior of the Sudler product of a badly approximable number and showed that the lower bound tends to 0 and the upper bound tends to infinity when the sequence of partial quotients in the continued fraction expansion of the number exceeds 7 infinitely often. This improves upon previous results for both the general case and the special case of quadratic irrationals. Additionally, we proved that the threshold value of 7 is optimal, even when considering quadratic irrationals.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Mumtaz Hussain, Junjie Shi
Summary: The Jarnik-Besicovitch theorem is a fundamental result in metric number theory that deals with the Hausdorff dimension of certain limsup sets. This paper investigates a related problem of estimating the Hausdorff dimension of a liminf set and provides calculations and heuristics for the corresponding multiplicative set.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Boting Jia
Summary: The article discusses the properties and characteristics of EP operators, and describes when Toeplitz operators and weighted shifts possess the EP property. It also discusses a weaker operator property than the EP property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Luca Vincenzo Ballestra
Summary: This article introduces a new model of economic growth that takes into account the spatial dependence of worker and capital flows on salaries and returns. The findings from theoretical analysis and numerical simulations show that this model can capture interesting transitional dynamics that the standard model fails to capture.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abhishek Chaudhary
Summary: This paper considers the Cauchy problem for the nonlinear fractional conservation laws with stochastic forcing. The existence of desired kinetic solution and the convergence of the approximate viscous solutions to a kinetic solution are shown. Furthermore, the existence of an invariant measure under a nonlinearity-diffusivity condition is proved, and the uniqueness and ergodicity of the invariant measure are demonstrated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ryan J. Monroe, Bruce K. Geist, Steven W. Shaw
Summary: Centrifugal pendulum vibration absorbers are important for controlling torsional oscillations in internal combustion engines. This paper relaxes traditional assumptions and considers the complete system, studying the dynamic coupling between the base and pendulum systems. It identifies cut-out shapes that produce system brachistochrone curves, showing that system tautochrones have superior dynamic stability and vibration absorbing performance.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Adrien Seguret
Summary: This paper focuses on the mathematical modeling and solution of the optimal charging problem for a large population of plug-in electric vehicles (PEVs) with mixed state variables. It introduces a mean field assumption to describe the evolution interaction of the PEVs population. The optimal control of the mixed system's continuity equation under state constraints is investigated, and the existence of a minimum solution is proven. The solution is characterized as a weak solution of a system of two coupled partial differential equations: a continuity equation and a Hamilton-Jacobi equation. Regularity results of the optimal feedback control are provided.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Thang Pham
Summary: This paper presents new applications of the powerful framework developed by Bennett, Hart, Iosevich, Pakianathan, and Rudnev, which involve the product and quotient of distance sets, the L2 norm of the direction set, and the L2-norm of scales in difference sets.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Youssef Azouzi, Mohamed Amine Ben Amor, Dorsaf Cherif, Marwa Masmoudi
Summary: In this paper, we extend the concept of conditional supremum to the measure-free setting of Riesz spaces using the conditional expectation operator. We explore its properties and highlight its crucial role in generalizing results from various disciplines to the framework of Riesz spaces. We also demonstrate its application in finance for characterizing certain financial conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Review
Mathematics, Applied
Saddam Hussain, Gourav Arora, Rajesh Kumar
Summary: This article presents a new semi-analytical technique based on the homotopy analysis approach for solving linear or non-linear differential equations. The technique is compared to well-known approaches and shows improved accuracy and rapid convergence.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Walt van Amstel, Jan Harm van der Walt
Summary: This paper investigates the isomorphism relationship between Banach lattice and dual lattice on compact Hausdorff spaces, and presents some decomposition theorems and duality theories. The applications of direct and inverse limits in the category of vector lattices are also discussed.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Adi Glucksam, Leticia Pardo-Simon
Summary: This note investigates the asymptotic behavior of the number of maximum modulus points of an entire function in a disc of radius r. While Herzog and Piranian constructed an entire function for which this quantity is unbounded, it is still unknown whether it is possible for it to tend to infinity. In this paper, a transcendental entire function is constructed that is arbitrarily close to satisfying this property, providing strong evidence for a positive answer to this question.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Soumyarup Banerjee, Rajat Gupta, Rahul Kumar
Summary: In this article, we study transformation formulas of the zeta function at odd integers over an arbitrary number field, generalizing Ramanujan's identity. Our findings lead to a new number field extension of Eisenstein series satisfying a specific transformation. These results have important applications in understanding odd zeta values and Lambert series in any number field.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Zekeriya Ustaoglu
Summary: In this paper, we investigate the problem of determining a function from its surface integrals of the second type over n-dimensional circular paraboloids in Rn+1 with fixed focal length and fixed direction of symmetry axis. We obtain some inversion formulas with a method based on the Fourier transform and reducing the reconstruction problem to solving a Volterra integral equation of the first kind. We present some examples on the direct numerical implementations of the resulting inversion formulas.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
P. L. Robinson
Summary: This article presents explicit Weierstrassian expressions and duplication formulae for the generalized sine function sinp,q in the cases of (p, q) = (3 , 6) and (p, q) = (6/5 , 6).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sonia Foschiatti
Summary: This study considers the inverse problem of identifying the coefficients sigma and q of the equation div(sigma backward difference u) + qu = 0 simultaneously from the known Cauchy data set. The study derives a result of global Lipschitz stability in dimension n ≥ 3.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
